This invention relates generally to simultaneous orbit and attitude control for acquisition and maintenance techniques for individual satellites as well as for multiple satellites in a constellation or formation, in which Modern Feedback Control is used for determining precise real-time autonomous on-board navigation, attitude estimation and both orbit and attitude control. The orbit control function of this control system can place any satellite in any orbit position in a formation or in a constellation, including the acquisition of the initial distribution for the constellation/formation after satellite separation from launch vehicles, and can also maintain the constellation/formation distribution. The attitude control function simultaneously estimates the attitude state and acquires and maintains desired attitude, including providing the required attitude maneuvers. In formation flying this unified control system establishes and maintains the satellite separation and phasing with respect to the xe2x80x98head of the fleetxe2x80x99 satellite, and synchronizes the satellite orientations with respect to this xe2x80x98head of the fleetxe2x80x99.
The orbital control of satellites, in both geostationary orbits (GEO) and low-earth orbits (LEO), has primarily been ground-based. Orbit maintenance and station keeping have historically required involvement of Control Center personnel in all phases of operation. The computational burden for satellite control, including orbit analysis, maintenance and station keeping, has been on the ground computers. The ground computers provide both the off-line functions of orbit determination and maneuver planning as well as the on-line functions of commanding and telemetry processing.
With evolution of the concepts of operating large number of satellites in a constellation, attention has been focused on developing autonomous on-board orbit control system that removes the need for ground-based orbit control. One such design, shown in U.S. Pat. No. 6,089,507, provides for autonomous orbit control through modern feedback control, using GPS and a controller such as the Linear Quadratic Gaussian (LQG) with Loop Transfer Recovery (LTR) and/or H-infinity Controller.
Traditionally, all earth orbiting satellites have had some form of on-board attitude determination and control system. Many attitude determination systems used some form of attitude sensing devices, such as earth sensors, sun sensors, star trackers, gyroscopes, and the like to provide attitude information. Actuators, such as reaction wheels, momentum wheels, magnetic torquers and thrusters, used this information to provide the attitude control based on pre-programmed parameters.
Various methods have been studied for autonomous control of satellite navigation. U.S. Pat. No. 5,109,346 to Wertz discloses autonomous navigation control using Global Positioning Satellites (GPS) for orbit determination, and a method for providing orbital corrections. However, Wertz uses a non-feedback control system, which is subject to unstructured uncertainty. Additionally, Wertz is limited to real-time orbit and attitude determination, not real-time control and/or correction. Furthermore, position finding using GPS is known, as described for example, in U.S. Pat. No. 4,667,203 to Counselman, III.
Various methods have also been studied for developing the required relative dynamics and kinematics equations that are required for formation flying orbit and attitude control. For example, Bauer, F. H., Hartman, K., Forta, D., and Zuinn, D., in their paper xe2x80x9cAutonomous Navigation and Controlxe2x80x94Formation Flying in the 21st Century,xe2x80x9d present the coordinates for control of multiple satellites moving in formation, without providing any detail on the method of obtaining this information for implementation.
Similarly, in Wang and Hadaegh, xe2x80x9cCoordination and Control of Multiple Micro Spacecraft Moving in Formation,xe2x80x9d each of the spacecraft moving in formation is modeled as a rigid body with fixed center of mass, and various schemes for generating the desired formation pattern are discussed. While they provide explicit laws for formation-keeping and relative attitude alignment based on nearest neighbor-tracking, they do not study or provide any method of obtaining this measurement information nor the actual implementation.
For attitude control, systems were designed using other controllers, such as proportional-integral-derivative (PID) compensators using a variety of frequency response techniques. However, the PID design requires trade-offs with conflicting design objectives, such as gain margin and closed-loop bandwidth, until an acceptable controller is determined. When the control dynamics are complex, or poorly modeled, or when the performance specifications are particularly stringent, PID system performance erodes. In cases where optimal control design have been used, no measurement feedback was incorporated.
It is an object of the present invention to utilize modern advanced multivariable feedback control techniques in the design of an unified real-time on-board orbit and attitude control system using GPS feedback. For orbit control, the control techniques to be used are the LQG/LTR for orbit maintenance and Feedback Linearization Control for orbit acquisition. For attitude control, the control techniques to be used are the Nonlinear Lyapunov Control and Sliding Robust Control.
These more powerful design tools result in a higher level of satisfaction only if a solution exists to the problem being solved. Achieving both satisfactory performance limits and ascertaining the existence of a satisfactory controller involves using an optimization theory. Use of an optimization theory helps avoid searching for solutions to problems for which there are no solution. A further benefit of optimization is that it provides an absolute scale of merit against which any design can be measured. These more powerful design tools utilize modern advanced multivariable feedback control techniques.
This invention provides a unified orbit and attitude control system on-board a satellite in orbit, the system having two closed loop multivariable controllers, a receiver that receives data for both satellite position and orientation, and a converter that converts the orbit and attitude control problem into a state-space form. For orbit control, the converter converts the control problem into a tracking problem and a regulator problem in order to minimize the position error and velocity error between the body in motion and a target. For attitude control, the converter converts the satellite orientation of the various satellites in formation into a relative attitude state, and the regulator minimizes this relative error to track and maintain the desired attitude orientation. The receiver receives data from the Global Positioning Satellite System or other external location information provider. This data typically comes in the form of Code pseudorange, which provides the positioning information, and Phase pseudorange, which provides attitude information. Both the attitude and orbit controllers are modern feedback closed loop controllers.
This invention provides a combined orbit and attitude control system that uses the orbit state vector to describe the orbit control system and relative attitude kinematics to describe the attitude control system. Control is provided by modern advanced multivariable feedback control techniques, for example, linear quadratic Gaussian/loop transfer recovery (LQG/LTR) controller for orbit maintenance control, a feedback linearization controller for orbit acquisition control, and a Lyapunov controller for attitude control. These controllers enhance the control system performance by minimizing the control error and control effort. Additionally, the real time feedback control results in optimum implementation of an on-board autonomous control system.
Attitude determination and control for formation flying requires the additional development of the relative attitude dynamics and kinematics, since formation flying requires attitude control relative to a particular xe2x80x98leadxe2x80x99 satellite, or xe2x80x98fleet-headxe2x80x99. Additionally, optimum control of formation flying will require a unified and autonomous orbit and attitude control system, whereby the two optimally interact to provide the required separation and phasing in position and orientation.
In its simplest form, formation flying is the situation where a first body is generally following a second body, in direction, attitude and speed. Commonly seen in military aircraft, where multiple planes fly in a group, the group following a lead plane while spaced apart a predetermined distance, and the group of following planes duplicating the changes in attitude, speed and direction of the lead plane. The lead body in a formation can be any body in the group. The lead body can also be a phantom, or a phantom can take the place of any body in the group. A constellation is simply of group of bodies, which may or may not be in formation. For satellites, autonomous attitude control for formation control is the use of relative attitude kinematics and dynamics, described relative to a particular reference satellite system. A xe2x80x98head-of-fleetxe2x80x99 reference system is used, by which the attitude kinematics and dynamics of all satellites in the formation are transformed into the xe2x80x98head-of-fleetxe2x80x99 coordinate system. Reduction of the attitude kinematics and dynamics into this common reference frame makes it possible to design the attitude control system. Control implementation of the chaser body to track and maintain positional relationship with the leader generally will require knowledge of relative position and velocity of the chaser and the leader, the angular velocity of the chaser, the attitude control torque of the chaser, and the orbit control force of the leader. The attitude dynamics is non-linear, and the development of the relative attitude kinematics and dynamics involved defining an xe2x80x98Attitude Statexe2x80x99 consisting of both angular position and angular rates, and defining the attitude state in terms of both attitude angle and the angular rates. Since the attitude dynamics is nonlinear, nonlinear controllers, such as Lyapunov and Sliding controllers, are well suited for use in the controller.
Additionally, a method and apparatus are provided for autonomous orbital and attitude control for a satellite, providing both the strategy and the controller design to achieve these strategies while applying the concepts of modern control theory to the classical problem of orbital mechanics. Furthermore, an orbit control apparatus and method for converting the orbit control problem into 1) a tracking problem and 2) a regulator design problem is provided, where the control problem minimizes both position error and velocity error between the satellite (also known as the pursuer) and its target position in a formation. This target position is separated from the lead satellite according to predetermined requirements of the particular formation.
The present invention further provides an attitude control apparatus and method for converting a tracking problem into a regulator design problem by using relative attitude control, where the control problem minimizes both relative attitude angle error and angular velocity error between the pursuer satellite and the target attitude state as represented by the lead satellite in the formation. This target position can be the same attitude as the attitude of the lead satellite, or a commanded bias may be introduced.
The simultaneous elimination of these errors with minimum effort results in an optimal unified orbit and attitude control system. Both the orbital state and the attitude state of the member satellite is estimated from code pseudo-range and phase pseudo-range as derived from the Global Positioning System Satellites (GPS) using Kalman filtering techniques.
Additionally, the present invention provides for the use of positioning data from other sources, such as celestial measurements for estimating the orbital state of satellites, or use of Gyros/RMS for attitude estimation. Other sources of positioning data may be used, and the positioning data may be broadcast from other orbiting, flying or ground-based transmitters. Other sources of attitude information may be used, for example, Earth sensor, sun sensor or star tracker.
The control system of the invention uses four variations in the design of the controller to minimize the orbital error between a satellite and the target position in the orbit, and between the current attitude state and the target attitude state. These different design variations provide different levels of effectiveness caused by non-linearities and other systems uncertainties.
The object to be controlled does not have to be a satellite, but may be any body in motion needing attitude and/or trajectory adjustments.
The controller design preferably provides a GPS LQG/LTR autonomous orbit control and maintenance system for a multiple satellite formation, resulting in a measurement state feedback control design, consisting of a minimum variance estimator, for example, Kalman filter, and an optimal Linear Quadratic Regulator (LQR). Input to the regulator is the state estimate, and output of the regulator is the control law. The measurement controller is a linear quadratic Gaussian, LQG, controller. In order to increase robustness of the LQG controller, the loop transfer recovery (LTR) technique is used.
A second orbit controller design is provided implementing nonlinear feedback control using input/output feedback linearization controller. This is required to solve the nonlinear feedback problem for the case of satellite acquisition following separation from a launch vehicle. Initial acquisition of target positions following launch requires solving the nonlinear orbit control problem.
For attitude control, Lyapunov""s nonlinear controller is provided. Spacecraft attitude control for formation flying requires dealing with relatively large angle maneuvers and attitude and angular velocity tracking, and these involve nonlinear kinematics and dynamics. Hence, a nonlinear controller design is required. This controller uses the GPS Phase Pseudorange measurement as input into the feedback control operations. This controller is designed to track and correct the attitude state, consisting of both attitude angle and the angular rates.
A second controller design, the Sliding Robust Nonlinear Controller, is also provided. This controller is also an attitude and angular velocity tracking controller, using the nonlinear kinematics and dynamics equations that have been developed for attitude tracking and control for formation flying. Signals from GPS satellites, or alternatively from gyros/RMS or other like sources of positional information, are used to directly or indirectly determine the satellite attitude state. Furthermore, it is used in the real time feedback loop to continuously estimate the error between a satellite attitude and a target attitude. Both the Lyapunov controller and the sliding controller capture and track large angle slew maneuvers.
Orbit feedback information is used to generate thruster commands for correction of the satellite orbit in order to null the error. When this cycle is repeated, the desired orbit is maintained. Similarly, attitude feedback information is used to generate commands for attitude actuators, which may include momentum wheels or other gyros, reaction wheels, magnetic torquers, thrusters, gas jets, solar sails, and the like. When applied to multiple satellites in a satellite constellation or formation, attitude and orbit maintenance of individual satellites, as well as the separation and phasing between satellites operating in the constellation or formation, can be performed. Additionally, a group of satellites flying in a precise formation can be treated as a virtual satellite, that is, where a grouping of satellites appear to function as a single larger satellite, providing a virtual platform for imaging, observation, and the like.
The invention can also be applied to non-orbiting bodies such as aircraft, ground vehicles or sea vehicles operating in formation. The bodies may be moving under motive force or free falling.
It will be appreciated from the foregoing that the present invention represents a significant advance in the field of autonomous orbit and attitude control of satellites or bodies in formation and constellations. Other aspects of the invention will become apparent from the following more detailed description, taken in conjunction with the accompanying drawings,
Still other objects and advantages of the present invention will become readily apparent to those skilled in the art from the following detailed description, where we have shown and described only the preferred embodiments of the invention, simply by way of illustration of the best mode contemplated by us of carrying out our invention. As will be realized, the invention is capable of other and different embodiments, and its several details are capable of modifications in various respects, all without departing from the invention. Accordingly, the drawings and descriptions are to be regarded as illustrative in nature, and not as restrictive.